Problem: Rewrite the equation by completing the square. $4 x^{2} +8 x +3 = 0$ $(x + $
$\begin{aligned} 4 x^2 +8 x +3&=0 \\\\ 4 x^2 +8 x &=-3 \\\\ x^2 +2 x&=-\dfrac{3}{4} \end{aligned}$ Now we want to complete $x^2 +2 x$ into a perfect square. To do that, we should add $\left(\dfrac{{2}}{2}\right)^2={1}$ to it: $x^2{+2}x + {1}=\left(x +1 \right)^2$ $\begin{aligned} x^2 +2 x&=-\dfrac{3}{4} \\\\ x^2 +2 x + {1}&=-\dfrac{3}{4} + {1} \\\\ \left(x +1 \right)^2&=\dfrac{1}{4} \end{aligned}$ In conclusion, the equation after completing the square is written as: $\left(x +1 \right)^2=\dfrac{1}{4}$